We believe that the dichotomy established in Theorem REF  for the sets
\(\operatorname{A}_R(L)\)  also extends to the sets \(\operatorname{A}(L)\)  and \(I(L)\) . However, we were not able to
prove this. For the fast escaping set, such a result would follow
if every continuum in \(\operatorname{A}(f)\) 
(or every 'loop') would be contained in some level set \(\operatorname{A}_R^l(f)\) ,
which we also believe to be true (compare Question 2 and 3 in [1]}).
